A simple approach to asymptotic expansions for Fourier integrals of singular functions
Given the full asymptotic expansions for a Fourier integral \(\int_a^bf(x)e^{\pm isx}dx\) as \(s \to \infty,\) where \(s\) is real positive, \([a,b]\) is a finite interval, and the function \(f(x)\) may have different types of algebraic and logarithmic singularities at \(x=a\) and \(x=b.\) This problem has been treated in the literature by techniques involving neutralizers and Mellin transforms. In this paper, the relevant asymptotic expansions are received by a method that employs more simpler tools.
scientific article; zbMATH DE number 5757605
scientific article